Find the unit vector in the direction of \(-2i + 5j\).
Question 1 Report
Find the unit vector in the direction of \(-2i + 5j\).
Answer Details
To find the unit vector in the direction of \(-2i + 5j\), we need to first find the magnitude of the vector and then divide the vector by its magnitude.
The magnitude of the vector \(-2i + 5j\) is given by:
\begin{align*}
\sqrt{(-2)^2 + (5)^2} &= \sqrt{4+25} \\
&= \sqrt{29}
\end{align*}
Therefore, the unit vector in the direction of \(-2i + 5j\) is:
\begin{align*}
\frac{1}{\sqrt{29}}(-2i + 5j) &= \frac{1}{\sqrt{29}}\begin{pmatrix}-2 \\ 5\end{pmatrix} \\
&= \frac{1}{\sqrt{29}}\begin{pmatrix}-2/1 \\ 5/1\end{pmatrix} \\
&= \boxed{\frac{1}{\sqrt{29}}(-2i + 5j)}
\end{align*}
Therefore, option (B) is the correct answer.
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